Second, the case of time-varying topology is investigated. The concepts and results about state based potential game proposed by J.R. Marden [1]} have been used and combined with our previous results. Similar to fixed topology case, a necessary and sufficient condition is also obtained. Certain state transition process is proposed as strategy depending Markov process, which assures the non-decreasing requirement of the state based potential function. An illustrative example is presented, which shows that the game theoretic control makes the multi-agent system reach consensus with probability 1.
